Non-Abelian geometric phases in ground-state Josephson devices

2010/02/28 by J.-M. Pirkkalainen, J. -M. Pirkkalainen, P. Solinas +4 · 2 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.supr-con #quant-ph

paper · pdf · doi:10.1103/physrevb.81.174506

published as Phys. Rev. B 81, 174506 (2010) · 5 pages, 3 figures; added references and clarified discussion about earlier research on the field

arxiv created 2010/04/07 · openalex publication_date 2010/05/05 · arxiv updated 2013/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a superconducting circuit in which non-Abelian geometric transformations can be realized using an adiabatic parameter cycle. In contrast to previous proposals, we employ quantum evolution in the ground state. We propose an experiment in which the transition from non-Abelian to Abelian cycles can be observed by measuring the pumped charge as a function of the period of the cycle. Alternatively, the non-Abelian phase can be detected using a single-electron transistor working as a charge sensor.

Citations

• Experimental Determination of the Berry Phase in a Superconducting Charge Pump
• Appearance of Gauge Structure in Simple Dynamical Systems
• Connecting Berry’s phase and the pumped charge in a Cooper pair pump
• Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
• Quantal phase factors accompanying adiabatic changes
• Suppression of the critical current of a balanced superconducting quantum interference device

Cited by

• Geometric quantum gates with superconducting qubits
• Experimental state control by fast non-Abelian holonomic gates with a superconducting qutrit